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UID:20260524T212652EDT-7771C1dTDA@132.216.98.100
DTSTAMP:20260525T012652Z
DESCRIPTION:Abstract\n\nThe modelling of linear quadratic Gaussian optimal 
 control problems on large complex networks is intractable computationally.
 \n\nGraphon theory provides an approach to overcome these issues by defini
 ng limit objects for infinite sequences of graphs. This permits one to app
 roximate arbitrarily large networks by infinite dimensional operators. Thi
 s is extended to stochastic systems by the use of Q-noise\, a generalizati
 on of Wiener processes in finite dimensional spaces to processes in functi
 on spaces. This thesis concerns the synthesis of two types of stochastic s
 ystem on large graphs: linear quadratic Gaussian problems with estimation 
 and linear quadratic field tracking games.\n\nThe optimal control and esti
 mation of linear quadratic problems on graphon systems with Q-noise distur
 bances are defined here and shown to be the limit of the corresponding fin
 ite graph optimal control problem. The theory is extended to low rank syst
 ems\, and a fully worked special case is presented. In addition\, the wors
 t-case long-range average and infinite horizon discounted optimal control 
 performance with respect to Q-noise distribution are computed for a set of
  standard graphon limits. The convergence of finite network linear system 
 state estimates to their graphon limit counterparts is established. Comput
 ational examples of this convergence behaviour is illustrated with a set o
 f standard graphon examples.\n\nIn this thesis\, linear quadratic games on
  very large dense networks are modelled with discrete time linear quadrati
 c graphon field games with Q-noise. In such a game\, the agents are interc
 onnected via an undirected network with one agent per node. Gaussian distu
 rbances that are correlated over nodes affect each agent. The limit of the
  finite-sized linear quadratic network tracking game in discrete time is f
 ormulated\, and it is shown that under the proper assumptions\, the game h
 as a graphon limit system with Q-noise. Then\, the optimal control of the 
 discrete time system is found in closed-form and the Nash equilibrium beha
 vior of the game is demonstrated numerically. The infinite time horizon di
 scounted case is also analyzed\, and a closed form feedback solution is pr
 esented in the special case where the underlying graphon is finite rank.\n
DTSTART:20250228T153000Z
DTEND:20250228T173000Z
LOCATION:Room 603\, McConnell Engineering Building\, CA\, QC\, Montreal\, H
 3A 0E9\, 3480 rue University
SUMMARY:PhD defence of Alex Dunyak – Stochastic Mean Field Control and Game
 s on Graph Limits: a Q-noise Formulation
URL:https://www.mcgill.ca/ece/channels/event/phd-defence-alex-dunyak-stocha
 stic-mean-field-control-and-games-graph-limits-q-noise-formulation-363794
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